Search results for "algebra"

New applications of graded Lie algebras to Lie algebras, generalized Lie algebras and cohomology

2007

We give new applications of graded Lie algebras to: identities of standard polynomials, deformation theory of quadratic Lie algebras, cyclic cohomology of quadratic Lie algebras, $2k$-Lie algebras, generalized Poisson brackets and so on.

Minimal number of periodic orbits for nonsingular Morse-Smale flows in odd dimension

2020

We compute the minimal number p_min of closed orbits of any Morse-Smale flow on any compact odd-dimensional manifold with boundary in terms of some given homological information. The underlying algorithm is based on optimization theory in network flows and transport systems. Such a number p_min is a lower bound in the general case but we provide, for any initial homological data, a Morse-Smale model for which p_min is attained. We also apply our techniques to the problem of the continuation of Lyapnov graphs to Lyapnov graphs of Smale type.

Integrable Systems and Factorization Problems

2002

The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without special knowledge of Geometry and Lie Groups. In order to make the main ideas reasonably clear, I tried to use only matrix algebras such as $\frak{gl}(n)$ and its natural subalgebras; Lie groups used are either GL(n) and its subgroups, or loop groups consisting of matrix-valued functions on the circle (possibly admitting an extension to parts of the Riemann sphere). I hope this makes the environment sufficiently easy to live in for an analyst. The main goal is…

Vibrational Spectrum of Phosphine Molecule

2004

Vibrational interactions and resonances in XY2 molecules of C2v symmetry. Algebraic application to D2S system.

2008

Scaling behavior of Tan's contact for trapped Lieb-Liniger bosons: From two to many

2018

We show that the contact parameter of N harmonically trapped interacting one-dimensional bosons at zero temperature can be analytically and accurately obtained by a simple rescaling of the exact two-boson solution, and that N-body effects can be almost factorized. The small deviations observed between our analytical results and density matrix renormalization group (DMRG) calculations are more pronounced when the interaction energy is maximal (i.e., at intermediate interaction strengths) but they remain bounded by the large-N local-density approximation obtained from the Lieb-Liniger equation of state stemming from the Bethe ansatz. The rescaled two-body solution is so close to the exact one…

Inside Back Cover: First Step Towards a Devil's Staircase in Spin-Crossover Materials (Angew. Chem. Int. Ed. 30/2016)

2016

International audience; Periodic and aperiodic spin-state concentration waves form during “Devil's staircase”-type spin-crossover in a new bimetallic 2D coordination polymer {Fe[(Hg(SCN)3)2](4,4′-bipy)2}n. In their Communication on page 8675 ff., J. A. Real, E. Collet et al. describe the appearance of spin-state concentration waves between long-range spatially ordered structures of low- and high-spin states during multistep spin-crossover.

Antoine Traisnel, Capture: American Pursuits and the Making of a New Animal Condition

2021

You can’t judge a book by its cover. Or so they say. But the cover of Antoine Traisnel’s Capture: American Pursuits and the Making of a New Animal Condition is striking and, one is tempted to say, captivating. And so is the book. The cover features colorful images of various birds—such as the ruby-throated hummingbird, the tufted coquette or the buff-tailed sicklebill—taken from one of the most impressive plates in Ernst Haeckel’s Kunstformen der Natur (Art Forms in Nature) and interlaced on ...

Delineating Aspects of Understanding Eigentheory through Assessment Development

2018

International audience; In this report, we share insights we have gained from developing an assessment for documenting students' understanding of eigentheory. We explain the literature and theory that influenced the assessment's development and share question examples. We frame our results in terms of three eigentheory settings (Ax = λx, (A - λI)x = 0, and eigenspaces) and four interpretations (numeric, algebraic, geometric, and verbal). Results from our analysis include students' reasoning being influenced by setting, insights into students' struggle with understanding eigenspaces, and the importance of making connections between and across various interpretations.

Guide pour l'ergonomie des interfaces homme-machine

1998

Rapport de contrat Bull INRIA; Spécifications ergonomiques pour la conception des interfaces logicielles Bull